Deep Spectral Clustering via Joint Spectral Embedding and Kmeans

TL;DR

This paper introduces Deep Spectral Clustering (DSC), a method that jointly optimizes spectral embedding and clustering using deep neural networks and greedy strategies, overcoming high-dimensional graph construction issues.

Contribution

The paper proposes an end-to-end deep spectral clustering framework that combines spectral embedding learning and greedy Kmeans optimization, improving clustering performance.

Findings

Achieves state-of-the-art results on seven real-world datasets.

Effectively handles high-dimensional data without explicit similarity graph construction.

Joint optimization enhances clustering accuracy.

Abstract

Spectral clustering is a popular clustering method. It first maps data into the spectral embedding space and then uses Kmeans to find clusters. However, the two decoupled steps prohibit joint optimization for the optimal solution. In addition, it needs to construct the similarity graph for samples, which suffers from the curse of dimensionality when the data are high-dimensional. To address these two challenges, we introduce \textbf{D}eep \textbf{S}pectral \textbf{C}lustering (\textbf{DSC}), which consists of two main modules: the spectral embedding module and the greedy Kmeans module. The former module learns to efficiently embed raw samples into the spectral embedding space using deep neural networks and power iteration. The latter module improves the cluster structures of Kmeans on the learned spectral embeddings by a greedy optimization strategy, which iteratively reveals the direction of the worst cluster structures and optimizes embeddings in this direction. To jointly optimize spectral embeddings and clustering, we seamlessly integrate the two modules and optimize them in an end-to-end manner. Experimental results on seven real-world datasets demonstrate that DSC achieves state-of-the-art clustering performance.